#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief SGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors f or GE matrices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGEES + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI, */ /* VS, LDVS, WORK, LWORK, BWORK, INFO ) */ /* CHARACTER JOBVS, SORT */ /* INTEGER INFO, LDA, LDVS, LWORK, N, SDIM */ /* LOGICAL BWORK( * ) */ /* REAL A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ), */ /* $ WR( * ) */ /* LOGICAL SELECT */ /* EXTERNAL SELECT */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGEES computes for an N-by-N real nonsymmetric matrix A, the */ /* > eigenvalues, the real Schur form T, and, optionally, the matrix of */ /* > Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). */ /* > */ /* > Optionally, it also orders the eigenvalues on the diagonal of the */ /* > real Schur form so that selected eigenvalues are at the top left. */ /* > The leading columns of Z then form an orthonormal basis for the */ /* > invariant subspace corresponding to the selected eigenvalues. */ /* > */ /* > A matrix is in real Schur form if it is upper quasi-triangular with */ /* > 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the */ /* > form */ /* > [ a b ] */ /* > [ c a ] */ /* > */ /* > where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBVS */ /* > \verbatim */ /* > JOBVS is CHARACTER*1 */ /* > = 'N': Schur vectors are not computed; */ /* > = 'V': Schur vectors are computed. */ /* > \endverbatim */ /* > */ /* > \param[in] SORT */ /* > \verbatim */ /* > SORT is CHARACTER*1 */ /* > Specifies whether or not to order the eigenvalues on the */ /* > diagonal of the Schur form. */ /* > = 'N': Eigenvalues are not ordered; */ /* > = 'S': Eigenvalues are ordered (see SELECT). */ /* > \endverbatim */ /* > */ /* > \param[in] SELECT */ /* > \verbatim */ /* > SELECT is a LOGICAL FUNCTION of two REAL arguments */ /* > SELECT must be declared EXTERNAL in the calling subroutine. */ /* > If SORT = 'S', SELECT is used to select eigenvalues to sort */ /* > to the top left of the Schur form. */ /* > If SORT = 'N', SELECT is not referenced. */ /* > An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if */ /* > SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex */ /* > conjugate pair of eigenvalues is selected, then both complex */ /* > eigenvalues are selected. */ /* > Note that a selected complex eigenvalue may no longer */ /* > satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since */ /* > ordering may change the value of complex eigenvalues */ /* > (especially if the eigenvalue is ill-conditioned); in this */ /* > case INFO is set to N+2 (see INFO below). */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA,N) */ /* > On entry, the N-by-N matrix A. */ /* > On exit, A has been overwritten by its real Schur form T. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] SDIM */ /* > \verbatim */ /* > SDIM is INTEGER */ /* > If SORT = 'N', SDIM = 0. */ /* > If SORT = 'S', SDIM = number of eigenvalues (after sorting) */ /* > for which SELECT is true. (Complex conjugate */ /* > pairs for which SELECT is true for either */ /* > eigenvalue count as 2.) */ /* > \endverbatim */ /* > */ /* > \param[out] WR */ /* > \verbatim */ /* > WR is REAL array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] WI */ /* > \verbatim */ /* > WI is REAL array, dimension (N) */ /* > WR and WI contain the real and imaginary parts, */ /* > respectively, of the computed eigenvalues in the same order */ /* > that they appear on the diagonal of the output Schur form T. */ /* > Complex conjugate pairs of eigenvalues will appear */ /* > consecutively with the eigenvalue having the positive */ /* > imaginary part first. */ /* > \endverbatim */ /* > */ /* > \param[out] VS */ /* > \verbatim */ /* > VS is REAL array, dimension (LDVS,N) */ /* > If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur */ /* > vectors. */ /* > If JOBVS = 'N', VS is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVS */ /* > \verbatim */ /* > LDVS is INTEGER */ /* > The leading dimension of the array VS. LDVS >= 1; if */ /* > JOBVS = 'V', LDVS >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (MAX(1,LWORK)) */ /* > On exit, if INFO = 0, WORK(1) contains the optimal LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. LWORK >= f2cmax(1,3*N). */ /* > For good performance, LWORK must generally be larger. */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; the routine */ /* > only calculates the optimal size of the WORK array, returns */ /* > this value as the first entry of the WORK array, and no error */ /* > message related to LWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] BWORK */ /* > \verbatim */ /* > BWORK is LOGICAL array, dimension (N) */ /* > Not referenced if SORT = 'N'. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > > 0: if INFO = i, and i is */ /* > <= N: the QR algorithm failed to compute all the */ /* > eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI */ /* > contain those eigenvalues which have converged; if */ /* > JOBVS = 'V', VS contains the matrix which reduces A */ /* > to its partially converged Schur form. */ /* > = N+1: the eigenvalues could not be reordered because some */ /* > eigenvalues were too close to separate (the problem */ /* > is very ill-conditioned); */ /* > = N+2: after reordering, roundoff changed values of some */ /* > complex eigenvalues so that leading eigenvalues in */ /* > the Schur form no longer satisfy SELECT=.TRUE. This */ /* > could also be caused by underflow due to scaling. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2017 */ /* > \ingroup realGEeigen */ /* ===================================================================== */ /* Subroutine */ int sgees_(char *jobvs, char *sort, L_fp select, integer *n, real *a, integer *lda, integer *sdim, real *wr, real *wi, real *vs, integer *ldvs, real *work, integer *lwork, logical *bwork, integer * info) { /* System generated locals */ integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3; /* Local variables */ integer ibal; real anrm; integer idum[1], ierr, itau, iwrk, inxt, i__; real s; integer icond, ieval; extern logical lsame_(char *, char *); logical cursl; integer i1, i2; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), sswap_(integer *, real *, integer *, real *, integer * ); logical lst2sl; extern /* Subroutine */ int slabad_(real *, real *); logical scalea; integer ip; real cscale; extern /* Subroutine */ int sgebak_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, integer *), sgebal_(char *, integer *, real *, integer *, integer *, integer *, real *, integer *); extern real slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int sgehrd_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *), xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); real bignum; extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *); logical lastsl; extern /* Subroutine */ int sorghr_(integer *, integer *, integer *, real *, integer *, real *, real *, integer *, integer *), shseqr_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, real *, real *, integer *, real *, integer *, integer *); integer minwrk, maxwrk; real smlnum; integer hswork; extern /* Subroutine */ int strsen_(char *, char *, logical *, integer *, real *, integer *, real *, integer *, real *, real *, integer *, real *, real *, real *, integer *, integer *, integer *, integer * ); logical wantst, lquery, wantvs; integer ihi, ilo; real dum[1], eps, sep; /* -- LAPACK driver routine (version 3.7.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* June 2017 */ /* ===================================================================== */ /* Test the input arguments */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --wr; --wi; vs_dim1 = *ldvs; vs_offset = 1 + vs_dim1 * 1; vs -= vs_offset; --work; --bwork; /* Function Body */ *info = 0; lquery = *lwork == -1; wantvs = lsame_(jobvs, "V"); wantst = lsame_(sort, "S"); if (! wantvs && ! lsame_(jobvs, "N")) { *info = -1; } else if (! wantst && ! lsame_(sort, "N")) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*lda < f2cmax(1,*n)) { *info = -6; } else if (*ldvs < 1 || wantvs && *ldvs < *n) { *info = -11; } /* Compute workspace */ /* (Note: Comments in the code beginning "Workspace:" describe the */ /* minimal amount of workspace needed at that point in the code, */ /* as well as the preferred amount for good performance. */ /* NB refers to the optimal block size for the immediately */ /* following subroutine, as returned by ILAENV. */ /* HSWORK refers to the workspace preferred by SHSEQR, as */ /* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */ /* the worst case.) */ if (*info == 0) { if (*n == 0) { minwrk = 1; maxwrk = 1; } else { maxwrk = (*n << 1) + *n * ilaenv_(&c__1, "SGEHRD", " ", n, &c__1, n, &c__0, (ftnlen)6, (ftnlen)1); minwrk = *n * 3; shseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[1] , &vs[vs_offset], ldvs, &work[1], &c_n1, &ieval); hswork = work[1]; if (! wantvs) { /* Computing MAX */ i__1 = maxwrk, i__2 = *n + hswork; maxwrk = f2cmax(i__1,i__2); } else { /* Computing MAX */ i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1, "SORGHR", " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen) 1); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n + hswork; maxwrk = f2cmax(i__1,i__2); } } work[1] = (real) maxwrk; if (*lwork < minwrk && ! lquery) { *info = -13; } } if (*info != 0) { i__1 = -(*info); xerbla_("SGEES ", &i__1, (ftnlen)5); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { *sdim = 0; return 0; } /* Get machine constants */ eps = slamch_("P"); smlnum = slamch_("S"); bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); smlnum = sqrt(smlnum) / eps; bignum = 1.f / smlnum; /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */ anrm = slange_("M", n, n, &a[a_offset], lda, dum); scalea = FALSE_; if (anrm > 0.f && anrm < smlnum) { scalea = TRUE_; cscale = smlnum; } else if (anrm > bignum) { scalea = TRUE_; cscale = bignum; } if (scalea) { slascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, & ierr); } /* Permute the matrix to make it more nearly triangular */ /* (Workspace: need N) */ ibal = 1; sgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr); /* Reduce to upper Hessenberg form */ /* (Workspace: need 3*N, prefer 2*N+N*NB) */ itau = *n + ibal; iwrk = *n + itau; i__1 = *lwork - iwrk + 1; sgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, &ierr); if (wantvs) { /* Copy Householder vectors to VS */ slacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs) ; /* Generate orthogonal matrix in VS */ /* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */ i__1 = *lwork - iwrk + 1; sorghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk], &i__1, &ierr); } *sdim = 0; /* Perform QR iteration, accumulating Schur vectors in VS if desired */ /* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */ iwrk = itau; i__1 = *lwork - iwrk + 1; shseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[1], &vs[ vs_offset], ldvs, &work[iwrk], &i__1, &ieval); if (ieval > 0) { *info = ieval; } /* Sort eigenvalues if desired */ if (wantst && *info == 0) { if (scalea) { slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wr[1], n, & ierr); slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wi[1], n, & ierr); } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { bwork[i__] = (*select)(&wr[i__], &wi[i__]); /* L10: */ } /* Reorder eigenvalues and transform Schur vectors */ /* (Workspace: none needed) */ i__1 = *lwork - iwrk + 1; strsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset], ldvs, &wr[1], &wi[1], sdim, &s, &sep, &work[iwrk], &i__1, idum, &c__1, &icond); if (icond > 0) { *info = *n + icond; } } if (wantvs) { /* Undo balancing */ /* (Workspace: need N) */ sgebak_("P", "R", n, &ilo, &ihi, &work[ibal], n, &vs[vs_offset], ldvs, &ierr); } if (scalea) { /* Undo scaling for the Schur form of A */ slascl_("H", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, & ierr); i__1 = *lda + 1; scopy_(n, &a[a_offset], &i__1, &wr[1], &c__1); if (cscale == smlnum) { /* If scaling back towards underflow, adjust WI if an */ /* offdiagonal element of a 2-by-2 block in the Schur form */ /* underflows. */ if (ieval > 0) { i1 = ieval + 1; i2 = ihi - 1; i__1 = ilo - 1; /* Computing MAX */ i__3 = ilo - 1; i__2 = f2cmax(i__3,1); slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ 1], &i__2, &ierr); } else if (wantst) { i1 = 1; i2 = *n - 1; } else { i1 = ilo; i2 = ihi - 1; } inxt = i1 - 1; i__1 = i2; for (i__ = i1; i__ <= i__1; ++i__) { if (i__ < inxt) { goto L20; } if (wi[i__] == 0.f) { inxt = i__ + 1; } else { if (a[i__ + 1 + i__ * a_dim1] == 0.f) { wi[i__] = 0.f; wi[i__ + 1] = 0.f; } else if (a[i__ + 1 + i__ * a_dim1] != 0.f && a[i__ + ( i__ + 1) * a_dim1] == 0.f) { wi[i__] = 0.f; wi[i__ + 1] = 0.f; if (i__ > 1) { i__2 = i__ - 1; sswap_(&i__2, &a[i__ * a_dim1 + 1], &c__1, &a[( i__ + 1) * a_dim1 + 1], &c__1); } if (*n > i__ + 1) { i__2 = *n - i__ - 1; sswap_(&i__2, &a[i__ + (i__ + 2) * a_dim1], lda, & a[i__ + 1 + (i__ + 2) * a_dim1], lda); } if (wantvs) { sswap_(n, &vs[i__ * vs_dim1 + 1], &c__1, &vs[(i__ + 1) * vs_dim1 + 1], &c__1); } a[i__ + (i__ + 1) * a_dim1] = a[i__ + 1 + i__ * a_dim1]; a[i__ + 1 + i__ * a_dim1] = 0.f; } inxt = i__ + 2; } L20: ; } } /* Undo scaling for the imaginary part of the eigenvalues */ i__1 = *n - ieval; /* Computing MAX */ i__3 = *n - ieval; i__2 = f2cmax(i__3,1); slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ieval + 1], &i__2, &ierr); } if (wantst && *info == 0) { /* Check if reordering successful */ lastsl = TRUE_; lst2sl = TRUE_; *sdim = 0; ip = 0; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { cursl = (*select)(&wr[i__], &wi[i__]); if (wi[i__] == 0.f) { if (cursl) { ++(*sdim); } ip = 0; if (cursl && ! lastsl) { *info = *n + 2; } } else { if (ip == 1) { /* Last eigenvalue of conjugate pair */ cursl = cursl || lastsl; lastsl = cursl; if (cursl) { *sdim += 2; } ip = -1; if (cursl && ! lst2sl) { *info = *n + 2; } } else { /* First eigenvalue of conjugate pair */ ip = 1; } } lst2sl = lastsl; lastsl = cursl; /* L30: */ } } work[1] = (real) maxwrk; return 0; /* End of SGEES */ } /* sgees_ */